One of our dgraphs has the following parameters -
--back_compat 601
--back_compat 610
--back_compat 614

Is there any known performance issues or has anyone a bad experience setting these flags? We're seeing some performance slowness with regards to navigation requests and I wonder if setting these might be a cause for our performance degradation.

While I can't say with 100% certainty, I seriously doubt these flags have any impact on performance. The backward compatibility flags were built in so that customers could upgrade their version of the MDEX without having to upgrade their API logic on the front end (back two releases maximum). These flags instruct the MDEX to allow some older, possibly depricated, filter syntax to be processed. Therefore, my strong suspicion is that these flags themselves will have no impact on performance itself. The features you're using in the MDEX along with your data volume, data characteristics, and hardware/network will continue to be the main drivers for performance.